peter took a 1,500 mile trip in 5 days. each day, he drove 30 miles more than the day before. how many miles did he cover on the first day?
You have an arithmetic series,
where d = 30 , and Sum(5) = 1500 , a is first term
sum(n) = (n/2)(2a + (n-1)d)
1500 = (5/2)(2a + 120)
600 = 2a+120
2a=480
a = 240
On the first day he went 240 miles
check: 240 + 270 + 300 + 330 + 360 = 1500
To find out how many miles Peter covered on the first day, we can make use of the fact that each day he drove 30 miles more than the previous day.
Let's assume that on the first day, Peter drove x miles. Then, on the second day, he drove x + 30 miles. On the third day, he drove x + 30 + 30 miles (or x + 60 miles), and so on.
Since Peter took a 1,500 mile trip in 5 days, we can express the total distance he covered as the sum of the distances he covered each day:
x + (x + 30) + (x + 60) + (x + 90) + (x + 120) = 1500
Now, let's solve this equation to find the value of x, which represents the distance covered on the first day.
Rearranging the equation, we have:
5x + 300 = 1500
Subtracting 300 from both sides of the equation, we get:
5x = 1200
Dividing both sides of the equation by 5, we have:
x = 240
Therefore, Peter covered 240 miles on the first day.